Question

The pulley and strings shown in the figure below are massless. Find the Acceleration of system.
(Take $g=10{\text{m/s}}^2$)

• A. $2{\text{m/s}}^2$
• B. $1{\text{m/s}}^2$
• C. $1.5{\text{m/s}}^2$
• D. $2.5{\text{m/s}}^2$

Answer 1

The correct option is B $1{\text{m/s}}^2$

Let us suppose acceleration of blocks be $a$.
From the data shown in the figure

On applying $\sum F=ma$ for all the three blocks we get,
$10-T_1=1\times a...\left(1\right)$ [For block $A$]
$T_1-T_2-f_1=1\times a...\left(2\right)$ [For block $B$]
$T_2-f_2=1\times a...\left(3\right)$ [For block $C$]
On adding (1), (2) and (3), we get
$10-f_1-f_2=3\times a$
Limiting friction of block B:
$f_1=\mu N_1=0.35\times 10=3.5\text{N}$
Limiting friction of block C:
$f_2=\mu N_2=0.35\times 10=3.5\text{N}$
$\Rightarrow a=\frac{10-2\times 3.5}{3}$
$\Rightarrow a=1{\text{m/s}}^2$
Hence, option(b) is the correct answer.